[racket] 80-bit precision in Racket

From: Hendrik Boom (hendrik at topoi.pooq.com)
Date: Tue Nov 13 10:15:39 EST 2012

On Sun, Nov 11, 2012 at 03:11:50PM +0400, Dmitry Pavlov wrote:
> Neil, Matthias,
> Certainly not #2, and I doubt that #4 is a problem for us
> (although it may be, buried somewhere in specific calculations).
> #1 and #3 definitely are our case. We are doing numerical
> integration of celestial bodies over large periods of time
> (100 years is a norm). The forces that act on bodies may be of
> quite different orders of magnitude: for example, for near-Earth
> objects the acceleration towards the Sun is about 2.9e-4 AU/days^2,
> while corrections for peculiar relativistic effects (Lense-Thirring
> acceleration etc.) can be as small as 1e-17 AU/days^2 (I do not
> have exact numbers now). And those effects must be taken
> into account. Yet the numerical integration procedure has its
> numerical inaccuracies, too. So when we integrate these
> accelerations over ten or more years, it sort of pushes the
> limit of double precision representation. Again, I do not
> (yet) have a precise mathematical proof of it, but it is
> more or less obvious that we need to try 80-bit at least.

Is it conceivable that you need multiple-precision fixed-point?

-- hendrik

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